Beware of the Small-World Neuroscientist

[...]the SW-ness parameter σ is a continuous, quantitative, measure defined as: σ=C∕CrandL∕Lrand i.e., the ratio between C and L normalized by the Lrand and Crand of a set of equivalent random networks (Humphries and Gurney, 2008). While there is no well-established criterion to choose a connectivity metric out of the many existing ones, different metrics lead to different connectivity patterns, which may be associated with different basic topological properties, affecting SW evaluation. [...]limitations in the reliability of link estimation (e.g., due to noise or common sources) may decrease L and increase C, by simply adding a few false positive connections, leading to the observation of SW even in regular or random networks (Bialonski et al., 2010). Current methodologies use random rewirings of observed connections, typically conserving the number of nodes and links and the degree distribution, but disregarding the effects of network size on the normalized C and L and the statistical properties of the random ensemble. [...]the WS mechanism does not reflect the formation of neural connections, suggesting that alternative references, possibly incorporating anatomical or functional constraints, may be more appropriate for normalizing brain networks, and other properties, e.g., link distribution, number of modules in the network, correlations in the number of links, may be conserved in the random versions of observed network structures.